GB2520057A - Method for Simulating and/or Controlling Fluid Injection - Google Patents

Abstract

A method for simulating and/or controlling consecutive flow of a plurality of fluids in a wellbore of arbitrary geometry, involves forming, using or providing a model or simulation of the wellbore, the model or simulation representing the wellbore as a plurality of segments or portions; determining and/or providing one or more frictionpressure drop components associated with at least one portion or segment of the wellbore for the plurality of fluids; and calculating pressure drop values for at least one segment or portion and/or between segments or portions using the one or more friction pressure drop components. Preferably, the method involves determining a pressure response during acid stimulation.

Description

Method for Smuating and/or ControThng fluid njection

HELD OF HE NVFNTON

he present nvent:on reateb to a method for bmLda1ng and/or earm othng two ow during consecutM9 injection of a piuraflty of fluids in a tormation and/or hi a weflbore, and hi particuar, though not exciusiv&y, to a method for simuating and/or controing fluki flow during acid stmdatiori of a formation.

BACKGROUND TO THE NVENTON

Moddhng and/or simuiaflng fLed flow during consecutive injection of a piuraflty of fluids in a webore and/or a reservoir may be required in a number of appcations.

One such apphcation reatss to acid stimulation of a reservoir. Add stimuietion is typicafly performed in owpermeahUity carbonate reservoirs, in order to increase the recovery of hydrocarbons from the reservor. Acid stimuiation comprises injecting an acid composition into the reservoir. The acid typicafly reads with components of the rock formation, such as carbonates, which dissorves the tormation mathx and increases its porosity, thus improving ofi recovery rates during subsequent production.

Acid stimulation may be a costiy procedure. ln order to optirnise fluid injection parameters. eg. during acid stimulation, and reduce costs and/or environmental impact, it is dedrabe to mod& and/or simulate fluid flow during fluid injection into the formation in order to optimise the process parameters.

Some known computer simulations assodated with acid stimulation are described in a number of documents such as US 8066072 (Maersk Oe & Gas NS), us 2010/0295125 (Didier Yu Ding et aL), US 6,749,022 (Schluniberger Technology Corporation), US 6196.318 (Mobfl Ofl Corporation), US 6668.922 (Schiurnberger Technology Corporation). US 7,561,998 (Schiumberger Technology Corporation), US 7;603,261 (Schiumberger Technology Corporation), US 7603,696 (BJ Services Company), US 7657415 (Schlumberoer Technology Corporation), US 7853,440 (institut Francds dv Petroie), and WO 2013/089897 (EnonMo.bfl Upstream Research Company et aL).

SUMMARY OF THE INVENTION

According to a first aspect of the present invention there is provided method for simulating and/or controlling flaw of a fluid in a wellbore Advantageously. t.he method may &rnuate and/or contro consecutive flow of a purallty of fluids in a wellbore.

The method may comprise forming or providing a model or simulation of the wellbore. the model or simulation representing the weilbore as a plurality of segments, cells or portions, hi other words, the model or simulation may partition or discretise the w&lhore. e.g. o produce a segmented weilbore model. The cells may comprise a plurahty of grid c&ls.

[he method rosy comprise calculating pressure drop values, such as pressure drop values for or over at east one, and preferably each segment, portion or call and/or baween segments, cells or portions.

The pressure drop v&ue may comprise at least a friction pressure dmp component (AP01).

The method may comprise calculating, determining and/or provkling one or more friction pressure drop components associated with at least one portion, cell or segment oF the w&lbore.

The method may comprise providing or inputting the friction pressure drop components, e.g. irdo a reservoir simulator..

The method may comprise processing or calculating the pressure drop values for one or more segments, cells or p;ortions using the one or more friction pressure drop components, wterein the pressure drop values may be processed or calculated using or by the reservoir simulator. The method may comprise determining a pressure response during a well intervention, such as an acid stimulation or fluid pumping well intervention. The reservoir nuiator may he configured to determine the pressure response.

The method may comprise setting and/or controPing at east one parameter or proper of the well intervention based on the simulation and/or model and/or output of the reservoir simulator, such as a pressure response, one or more surface or downhoie pressures, one or more flow rates, a valve operation amount and/or the hke.

The reservoir simulator will be herein understood as a modelling tool, typically a computer model and/or software, capable of calculating, modelling, and/or predicting flow of one or more fluids and/or mixtures of fluids in a reservoir and/or weHbore.

A number of commercially available simulators exist. A suitable example c4 such a smulator is:PI: by Schlumberger. These simulators are aimed at predicting the production of oil from a reservoir, and typically predict the flow of a fluid to and/or from a reserv&r based on a number uf parameters relating to the fluids and the wefihore.

Whe these simulators may he useful in determining the production of oil for a given reservoir, they have a number of limitations if the wellbore simulator is to be used to simulate or niod a weHbore intervention such as acid stimulation or another technique comprising fluid injection. For example, while existing simulators may he capable of calcukifing and/or factoring some parameters and/or components relating to pressure drop in the welihore. e.g. hydrostatic pressure drop and/or acceleration pressure drop, such simuators typicaily do not sufficenUy accurately calculate frithon pressure drop components based on the chemical nature of the fluids. This may lead to inaccurate predictions, particularly in connection with acid stimulation where a number of frictionaFtering additives may be used, such as drag reducing gels. Existing commercial reservoir simulators may also not be configured to model flow of fluid at different locations in the wefibore in e discretised manner, e.g. to track fluid displacement in a weilbore of arbitrary geometrv. This may be important when one or more sections of the wellbore exhibit an irregular profile. eg. a liner asscSt.ad with one or more weilbores The present inventors have discovered that Eclipse or other similar reservoir simulators used to determine the production from a welibore, can be modified and adapted to instead simulate or model such well intervention nrocesses, The output of such simulations or models can be used to control or set one or more control parameters ci' the well intervention of fluid flow process and/or to monitor the process against expected parameters, for example.

However, the modifications or non-standard operations of reservoir simulators such as Eclipse may be required in order to simulate well intervention or fluid flow applications to a satistacory accuracy.

For example, accounting for pressure drop due to fnction, e.g. based on the chemical nature of the fluid composition may improve the accuracy of the simulation and thereby any operational parameters, settings or decisions taken using the simulation or the model.

The pressure drop values may comprise one or more further pressure drop comoonents, sue-h as hydrostatic pressure drop and/or acceleration pressure drop (.AFGbi.

The method may comprise calculating fiction pressure drop (tP,) independently of and/or separately from the simulator. By such provision, accurate friction pressure drop values may be calculated, and may be subsequently utHised, e.g. by providing or inputting the friction pressure drop values into the simulator that may otherwise not be configured to account for friction pressure drop and/or inadequately account for fricdon pressure drop.

The friction pressure drop components may be comprised in and/or may be provided in the fbrm o[ one or more vertical flow profile (VFP) tabies.

The method may comprise determining or providing a plurality of friction pressure drop components or VIP tables IOr at least one and optionaUy each portion, ce or segment, wherein two or more or each friction pressure drop component or each VFP table may be accoSted with at least one of: a different fluid, a difidrent fluid composition, a different fluid concentration, a different pipe or liner geometry and/or the ike The method may comprise dynamicailyawitching, updating or selecting VFP tables and/or friction pressure drop components during operation or use of the model or simulation, for example, responsive to or dependent on chenoes in fluid, fluid composition, fluid concentration and/or the like.

The method may comprise calculating friction pressure drop components (AP.) using one or more equahons.

The method may comprise determining friction pressure drop components for one or more segments, ces or portions using one or more of: liner length. plastic viscosfty of the fluid, flthd flow velocity in the ppe yield point of the fluid, liner inside darnethr. liner outside diameter, diameter of an annulus. volumetric flow rate of the fluid, other dimensions of the liner or annulus, Fanning friction factor, density of the fluid, roughness, drag reducer shift parameter, and/or the like.

The method may comprise varying the fluid density for one or more and optionally each segment. ces or portion of the model or simulation, for example with tme, and/or fluid concentration and/or composdion. The fluid density may be varied depending on changes in a calcuiated or determined fluid composition or concentration for a given portion, ce or segment The density may be modelled by varying a property or parameter of the fluid in the simulation or model, such as concentration, e.g. a salt. concentration.

The method may comprise inputting externally calculated friction pressure drop components, e.g. by using VFP tables, in the simulator. By such provision, the simulator may process accurate values of pressure drop for a paftcuiar fluid oornpoaiUon, for example at a given moment time, and/or at a ocation, e.g. a portion.

cell or segment of the wellbore and/or reservoir.

ihe method may comprise noutting the friction pressure drop data into the resevor smulator manuay.

The method may comprise inputting the friction pressure drop. data into the reservoir simulator automatioay. e.g. using an algorithm, script, and/or software, The method may comprise determining, modelhng and/or hacking fluid fronts in the model or &muiation. This may be particulady important in fluid flow simulations in which fluids, such as acid and/or drag reducers or other modifiers. are inected. For exampie, different fluids may have different densIties and may affect properties such as hydrostatic pressure, and/or the flow distribution, e.g. as a result of change in fluid density or due to the acidization process.

The method may comprise modelllng. determining and/or tracking fluid fronts by representing a fluid front usng a tracer or tracer concentration. The rnodefflng and tracking ci fluid fronts may aow changes in properties such as fluid density, composition, concentration and/or the like to be determined for at least one and preferably each segment, cell or portion of the model or simulation, Processes that are dependent on the properties, such as the selection or switching of VFP tables or friction pressure drop components, can then be performed based on these properties. For example, the method may compnse switching or selecting a new VFP table and/or friction pressure drop component for a segment, cell or portion when the volumetric saturation of a fluid (e.g. mud, water, add of drag reducing agent) in a segment or cell is above a threshold, wherein the threshold is optionaliy lower than 100%, e.g. the threshold may be 80% or higher, preferably 90% or higher and most preferably 95%.

The method may comprise dynar. ically changing Dma steps used to recalculate evolving parameters during use or running of the model or simulation, e.g. to minimise numerical artefacts such as numerical diffusion. The change in time steps may be associated with or responsive to events, such as introduction of a new fluid, or drag reducer or when the concentration ol' a fluid or drag reducer changes. The time step racy be dependent on a pump rate of one or more injected fluids and/or a volume of a segment or portion.

The method may comprise taking into account the effect of the fluid on the wellbore and/or reservoir, The method may comprise modelling a dissolution, solution or other removal of parts of the geological formaton in which the welibore and/or reservoir is formed. The dissoluVon may comprIse an acid dissolution. The method may comprise modeUing the dissoluflor, solution or other removal by varying a porosity or permeabiitv parameter or perreahUity enhancement factor, and or a wormhale length associated with one or more reservoir urid cells, The variation in porosity may be respon&ve to the calculation, modelling or determination of the one. or more fluid front. The modelling of the dissolution. solution or other removal may comprise using a wormhole modeL A wormhole length for use in the wormhole model may be related to a permeability parameter or permeability enhancemerrt factor. The permeabilfty or permeability enhancement factor may be scaled by a scaling factor that may be related to the wormhoie length and/or one or more dimensions of the reservoir grid ce, e.g. the scailng factor may be proportional to the wornihoie length and inversely proporbonal to the one or moore d ensions of the reservoir grid ce (e.g. the largest of a heht. width or depth of the segment or portion).

The method may comprise simulating flow of a fluid in a weilbare and/or during injection of the fluid in the webore, e.g. during acki stimulation.

lb The method may comprise injecting the fluid in the weilbore and/or the formation. The method may comprise acid stimLilating the formation.

The formation may typically comprise a subterranean and/cr geological formation. The fOrmation may be or comprise a carbonate containing iormnatiort The method may comprise segmenting or partitioning at east one section of the weflhore and/or reservofr in one or more segments, ceils or portions in the model or simulation. The eilbora may be segmented numencaly. The method may comprise segmenting each of a piuraty of sections of the weilbore into a plurailty of segments or portions.

The method may comprise segmenting a main or vertical section of the weilhore into a plurailtv of segments, cells or portions in the model or simulation, The main or vertical seclion. of the weilbore may comprise and/or may be defined in the model or simulation as a section of the weilbora nearest an entry point thereof and/or nearest the surläce or uphole.

The method may compnse segmenting at least one irection section of the weilbore into a plurality of segments, cells or portions in the model or simulation. The injection section(s) of the weilbore may comprise and/or may be defined as a section of the weilbore directly connected to and/or branching off from the main or vertical section of the welihore. The injection section(s) of the wefibore may comprise and/or may be defined as a section of the wellbore in fluid communication with the formation and/or reservoir

I

One or more injection sections of the wefibore may oomprise at least one liner section (e.g. a section or portion within a hollow liner) and/or at least one annulus section. The llner may comprise a hollow tubular or conduit, The simulation or model may represent the inside of the liner as one or more llner segments, cells or portions. The simulation or model may represent the at. east one annulus section as one or more annulus segments. cells or portions. The ulation or model may represent one or more holes, apertures, passages and/or other fluid transport means in the liner (e.g. for allowing fluid flow between the inside of the hner -and the annulus around the liner) as one or more hole segments, cells or portions. The simulation or model may represent or model the one or more holes.

apertures, pass-ages and/or other bud transport means as an inflow control device (IOU) or valve.

The number of liner segments, cells and/cr portions may be equal to the number of annulus apertures or portions This may help with finding nurnehcai solutions using the model or simulation. The method may compnse defining or otherwise forming the holes or apertures automatically in the model or emulaton, e.q.

by using an external script.

The Uner may extend from a heel or first portion of the irection section of the w&lbore nearest an entry point thereof, to a toe or second portion of the injection section of the wellhore farthest from an enfly point thereof.

The method may comprise feeding fluid, e.g. stimulating fluid, from the heel or first portion of the iniection section of the weilbore.

The iniection section of the wellbore may comprise openings to allow passage of fluid, e.g. stimulating fluid, through the wellbore. Typically, the injection wellbore may comprise, openings configured to allow substantially unrestricted passage of fluid, e.g. stimulating fluid, through the wellbore The liner may comprise a noncemented liner.

The liner may comprise a plurality of holes formed in a wall of the liner.

The llner may define an annular space between the liner and the injection welibome. e.g. between en outer suriace of the liner and an inner surface of the injection section of the weilbore.

The method may comprise injecting a fluid, e.g. stimulating fluid, into the annular space through one or more of the plurality of holes in the liner, preferably through a plurality of holes.

The annular space may he provided substanUisily along an entire length of the iniection section of the welibore and/or liner.

The holes in the liner may be distributed such so that the total hole area per length unit of the liner may be greater at the toe or second portion of the injection weUhore and/or liner than at the heel or flist portion ar the injection section of the weUbore and/or liner.

In use, upon injection of a fluid, e.g. stirnuting Fluid, the flud, e.g. stimuiating fluid. may enter the annular space through holes near the heel or first portion of the injection section of the weUhore. In use, upon further injection of fluid, e.g. stimulating fluid. in the liner, the fluid, e.g. stimuting fluid, may travel inside the liner towards the toe or second portion of the injection section of the welibore and/or liner, Thus, in use, fluid, e.g. stimulating fluid, may progressively enter the annular space through a pluraUty oF holes in the liner as the fluid, e.g. stimulating fluid, travels towards the toe or second portion of the injection section of the well bore.

The kier may be substantially closed at one end thereof, e.g. at a toe or second end thereof. The liner may comprise a closure, e.g. an end cap, at a toe or second end thereof. By such provision, fluid, e.g. stimulating fluid, injected into the liner may exit the liner and/or enter the annular space through one or more of the plurality of holes in the liner.

The liner may comprise at least two holes arranged substantialiy diametricaUy opposite one another. Typically, the liner may comprise a plurality of sets of holes provided along a length of the liner. Each set of holes may comprise at east one pair of holes which may typically be arranged substantially diametricafly opposite one another. Each set of holes may comprise a plurality of pairs of holes, e.g. arranged substantially circumferentiary around the liner. Each pair of holes may typically be arranged substantially diametrically opposite one another.

The holes in the liner may be distributed such so that the total hole area per length unit of the liner may be greater at the toe or second portion of the inection weilbore than at the heel or first portion of the injection section of the wellbore.

The distance between successive sets of holes in a longitudinal direction may decrease from a heel or first portion to a toe or second portion of the injection section of the wellbore. Addtionafty, or alternatively, the size,, e.g.. diameter, of the holes may increase from a heel or first portion to a toe or second portion of the inJection section of the welibore. This may improve fluid, e.g. stimulating fluid, distribution along th.e length of the injection section of the wellhore by ensuring a more evenly distributed flow of fluid, e.g. stimulating fiuid, from the ner into the annular soace along a length of the ner. Wtthout wishing to be bound by theory, it is behaved that flow of flthd, e.g. stimulafing fluid, through holes at or near a heel or first portion of the injection well bore may decrease the pressure of fluid, e.g. afimulaing fluid, along the length of the hoer, thus reducing the flow of tkdd. e.g. stimulating fluid, into the annular space at or near a toe. or second portion of the iner. By increasing the hole area distribution towards a toe or second portion of the liner, a more even and/or better distributed flow of fluid, e.g. stimulating fluid. from the liner into the annular space may be obtained dong the length of the hoer.

lOan embodiment, the total hole area per length unit of the hoer at or near atoe or second portion of the injection weilbore may be at least two times. preferaby at east three bnes, more pretèrably at east or about four times the total hole area per length unit of the liner at or near a heel or first portion of the injection secton of the wehbore.

ln an embodiment, the holes in the liner may have a diameter in the range of about 4 mm to about 8 mm, e.g. about 5mm to about 7mm. typically about 6 mm..

rhe distance between consecutive holes in the liner at or near a second portion of the injection well bore may be ass than about 12 metres, preferably ass than about 9 metres, typically about 7.5 metres. The distance between consecutive holes in the liner at or near a first portion of the injection section of the wefibore may be greater than about 24 metres, preferabty greater than 27 metres, typicaily about 30 metres.

ln an embodiment, the bner may have a diameter, ag'. an inner diameter, of between about 11 cm to about 18cm.

The method may comprise providing, inputhng or communicating the parameters determined using the model or simulation into a controller for controing apparatus for performing a weilbore intervention, such as an acid stimulation and/or fluid injection or flow process. The apparatua may comprise one or more pumps and/or valves and/or pressure controllers.

According to a second aspect of the present invention there is provided a method for performing an acid stimulation operation, the method comprising modelling or niuiating a wehbore and/or reservoir using the method of the first aspect, and injecting acid into the using at east one parameter or setting determined From the model or simulation.

The at least one parameter or setting may comprise a flow rate of acid and/or drag reducer, and/or a pump rate, and/or an uphole or downho pressure. and/cr one or more valve openings and/or the like.

According to a third aspect of the present invention is a processing device or smulator for aimuiatng and/or modeing a wellbore, the processing device or simulator being configured to model or simulate the welFoore using the method of the first aspect.

The processing device or simulator may impiement a simulation module for forming a model or simulation of the well bore, the model or simulation representing the weHbore as a plurality of segments, oehs or portions. The simulation module may be configured to partition or thscretise the weUbore, The processing device or simulator may implement a calculation moduie fbi calculating or providing pressure drop vc&ues, such as pressure drop values for or over at least one, and preferably each segment or portion and/or between segments or portions.

The pressure drop vaiue may comprise at least a friction pressure drop component The processing device or simulator may be conrigured to implement a module for cacuabng determining and/or provthng one or more friction pressure drop wmponents associated with at least one portion or segment of the weilbore, The friction pressure drop components may he provided or input into a reservoir smuiator. The reservoir simulator may be implemented by the processing device and/or simulator.

The reservoir simulator may be configured to process or calculate the pressure drop values for one or more segments or portions using the one or more friction pressure drop components. The reservoir simulator may be configured to determine a pressure response during awell intervention, such as en acid stimulation or fluid pumping. The reservoir simulator may be configured to determine the pressure response.

The processing apparatus or simulator may be configured to set and/or control at east one parameter or property o? the well intervention based on the simulation and/or model and/or output of the reservoir simulator, such as a pressure response, one or more surface or downhole pressures, one or more flow rates, a valve operation amount and/or the like.

The processing device or simulator may comprise a uracessing unit and may comprise and/or be ccnhgured to communicate with a memory or data store, a display and/or s communications interface. The processing device or simulator may comprise and/or be configured to communicate with a controer for controlling apparatus [or

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periorming a welibore intervention or process. The apparatus may comprise one or more pumps, one or more velves, a pressure controer and/or the like.

Accord!ng to a fourth aspect of the present hvention is a controUer for controlling apparatus for performing a weilbore intervention or process, the oontroer comprisng or being configured to communicate wih the processing device according to the third aspect According to a fifth aspect of the present invenhon is a computer program product for at least partiafly, and cpllonay whoHy, implementing the method o the first and/or second aspects and/or the apparatus of the third and/or fourth aspects.

According to a sixth aspect of the present invention is a carrier medium or processing apparatus comprising or programmed with the computer program product of the fifth aspect.

The features described in relation to any other aspect or the invention, can appiy in respect of the method according to a second aspect of the present invention, and are therefore not repeated here for brevity.

BRIEF DESCRiPTION OF THE DRAWlNGS

These and other aspects of the present invention wiV now be described, by way of example ony, with reference to the accompanying drawings, in which: Figure 1 is a schematic Ulustrating an acid iniection process; Figure 2 is a schematic of apparatus for simuisting and/or controiling an acid injection according to an embodiment of the present invention; Fi$twe 3 is a flowchart illustrating a method of simuiating a wehore intervention in the fonn of an acid stimulation; FIgure 4 is a schematic of a model of a weilbore used in the method of Figure 3: Figure is an illustration of a method For accounting For a friction pressure drop component in the method o Figure 3; Fi9ure is a PrandWKarman plot that illustrates the effect of drag reduction; Figure 7 is a schematic iflustrathig the dynamic selection of suitable VFP tables to model for friction pressure drop in the method of Figure 3 using keywords petaining to the Eclipse &mulator; Figure is a schematic of a pump schedule invoMng different fluids. rates and concentrations; Figure is an ustration showing the effect of acid pump rate on wormhole growth; and Figure 10 a a graph showing the variation of modeHed and measured uphole and dowiihole pressures during anacid stmulation procedure, the modefled data being produced using the method of flgure 3.

DEtAiLED DESCRIPTiON OF THE DRAWINGS

Effective development of iowperrneahiiity carbonate reservoirs requires, among other factors, efficient we stimulation, This is often attempted using openhole add wash, add or san&propped fracturing in isolated zones or by buliTheading acid into slotted hriers. However, all of these methods suffer from either high *cost, inadequate or uneven akin reduction, or both.

Numeric rnodeiUng can be used to determine the conditions and operating parameters required to ensure the beat posaibie distribution of the acid, effective control ctt the wocinhole growth rate n muftiple sections of the we, displacement of mud along the entire reservoir section, handUng of significant (1,000+ psi) formation pressure gradients along the reservoir section, and many other complicating factors.

Embodhnents described herein model a matrixacid stimulation using a controhed acid jet (CAJ) liner The Embodiments described use the commercial reservoir simulator Eciipse in conjunction with external scnpting in order to provide a simulation of the acid stimulation process in an arbitrary weilbore. However, the design approach described here is by no means limited t.o the CM completion concept or the Eclipse reservoir simulator, and it will be appreciated that the concepts and techniques described herein are more widely appflcahle to other weilbora geometries and systems, fluid injection techniques and simulator packages.

In particular, understanding the pressure response durinc a well intervention is a key requirement for designing and Improving the well intervention job. interpretation of results from an acid treatment is generally difficult. For example, whUe it may he obvious that acid improves injectivity due to the chemical reaction with the carbonate rock, it may be less obvious how weD it does that and whether the same amount of acid could have been used more efficiently. e.g. by changing elements of the treatment design. Major steps fOrward in terms of improved stimuiation efficiency may be achieved with the aid of numerical modefling.

Figure 1 illustrates an example of a general acid stimulation process using a CM liner and associated technque. in this example, a wefibore system 5 comprise-s a horizontal wellhore 10 in a geological formation 15, The welibore system 5 further comprises a hollow liner 20, such as a tubular, sealed to a hollow casing 25, wherein the casing 25 is cemented into the wellbore 10. The liner 20 has a smaller outer diameter than the inner diameter of the casing 25, such that a portion of the liner 20 is provided within the casing 25. Seals 30, such as sweilable or expandable packers or other sealing mechanisms known in the art, are provided between the outer circumference of the liner 20 and en inner circumference of the casing 25.

The liner 20 comprises a series of openings or holes 35 along its length. The liner 20 is configured such that the prooortlon of the surface area. of liner 20 that is taken up by the openings 35 is greater toward the end 40 of the liner 20 furthest from the casing 25 than the end 45 of the finer 20 closer to the casing 25. The finer 20 is closed at the end 40 furthest from the casing 25.

An annular gap 50 is provided between the outer periohery of the liner 20 and the geological JOrnation 15 that defines the inner surface of the wellbore 10. Initially; at least a portion of this annular gap 50 and the intehor of the firer 20 is filled wiui rnudcake 55. Acid 60 is pumped down hole and into the liner 20, Under the action of the pumped ad 80, mud 55 is displaced through the liner 20 and ou through the openings 35 of the liner 20. The mud 55 initially clears from the. nnuu 50 at the end of the liner 20 closest to the casing 25 thereby forming an open space 65 in the annulus 50. in this space 65, acid 60 can be injected into the annulus 50 from the openings 35 at the casing end 45 of the liner 20. This acid 60 permeates into the geological formation 15 to react with suitable materials, such as carbonates, in order to stimulate the formation 15.

An interface 70 of breakdown mud cake fOrms between the open space 65 and the mudcake 55 in the remaining portion of the annulus 50. As the process continues, and more acid 60 is injected, then open space 65 expands toward the end 40 of the finer 20 furthest from the casing 25, with the interface 70 of broken down mudcake movhig with it, unt aU of the mud 55 has been displaced. it wfli be appreciated that, as the open space 55 expands toward the end 40 of the liner 20 furthest from the casing 25, more of the geological forniatfon 15 that forms the inner surface of the borehole 10 wl receive the acid treatment.

it will be appreciated that various parameters can be selected and/cr controlled in order to optimise this process, For example, the geometry of the liner 20. the arrangement of openings $5, the concentration, type and flow rate of the acid 00, the choice and concentration of process modifying fluids such as drag reducers (not shown), the rressure both downhole and at the surface, amongst other parameters.

can be selected or controed to optimise the process. Accurately modelling the welibore system S can be used to optimise at east sonic of these parameters.

It will be appreciated that the modelng process can he carried out using suitably programmed and configured computational apparatus 105, such as that shown in Figure 2, which comprises a processor 110. data storage 115 or memory, a display 120, one or more user input devices 125 such as a keyboard or mouse and a communications or network interface 130, Whilst some of the process features that can be. optimised involve apnaratus features, such as a liner 20 having the required geometry or arrangement of openings or holes 35. some of the process features that could he optimised are process 21) vadables that can be varied during operation, such as operation of pumps 135 for puming the acid to the liner and/or operation of any regulation valves 140, e.g. responsive to a suitable controller 145. It will be appreciated that the modelling process can contribute to optimisation both of selection of optimal apparatus and structural consideraUons and also the provision of optmai process variables, e.g. to the controller 45 from the computational apparatus 105.

The process of modelling the weilbore system 5 according to embodiments of the present invention is shown in Figure 3.

in step 205 a model 305 (see Figure 4) oF the weilbore system S is created.

The model 305 is formed by rapresenting the welibore system 5 by a series of so discretized cells 310a. 31Gb. 310c, each ccli 310a. 31Gb, 310c representing a pordon or segment of the weilbore system. This segmentation of the model of the wellhore system is particularly beneficial in tracking fluid fronts inside the weilbore system The cells 310a, Slob, 310c or segments can branch off from each other, which is useful wten modelling multiiaterai wells, but they can also rejoin a previous segment in a looped flow path. An example of a segmented model 305 of a welibore system 5 that comprises a wellbore 10 completed with a CAJ liner 20 is shown in Figure 4.

The numbering of the segments and theft branches is not important for solving the system. As can be seen from Figure 4. the tubing or casing 25 and the liner 20 are represented by one branch 315 with a number of segments or cells 3 IDa. The annulus is represented by another branch 320, also having a number of segments or cells SlOb.

A larger number of cells or segments 310a, 31Gb; Sloe enahies better fluid tracking, up to a certain point. Any pressure gauges are treated as separate segments to tacilltatc accurate comparison between modelled and measured pressure data.

The model of Figure 4 shows five segments 31 Go that represent inflow control devices (IC[)s). which are used to mimic the openings or holes 35 in the liner 20. Each cell or segment 3100 associated with an GO branches off from the liner 20 (main branch 315) and subsequently links to the branch 320 containing the annulus cells or segments 31Db. Creating this looped flow path can be performed as milows: I Create the main, branch 315 describing the casing 25 and the liner 20.

2. Create the annulus branch 320, which branches off from the main branch 315.

3. Create the lCD segments or cells. 31 Go. which also branch off from the main branch. 315.

4. Link each lCD segment or cell SiOc with the corresponding annulus segment or ce 31Db.

5. Link each annulus segment or cell SIGh with the appropriate reservoir grid cell(s).

The input required for defining the cells or segments SiOa. 31Gb, 310c in this particuthr example includes depth (both MD and TVD), diameter (one inner diameter for flow in the liner and two diameters for annular flow, i.e. the outer diameter of the liner 20 and the inner diameter of the wellbore 10)! length, volume, roughness and optionally also thermai input. The lODs are characterised by their hole size and discharge coefficient.

For a liner cell or segment 310a; a reservoir simulator such as Eclipse can be used to calcuiate the volume correctiy, but the volume of the annulus segments 31Db may require to be provided by other means such as custom scripting. Optionally, the model 305 can also be set up with thermal input.

In specific optional embodiments. an equal number of ilner and annulus segments or cells 31Cc, SlOb are provided. it has been found that this 1:1 ratio facilitates the subsequent segment linking process.

A typical CM Uner 20 consists of more than two hundred openings or holes 35, so a high degree of automabon, e.g. via scdpting, may he necessary to make the input generation manageable The segments or cells 31Cc containing an opening or hole 35 are modelled to have a iength comparable t.o the ho or opening size. This means that additional segments or cells are required to cover the distance between the holes/openings 35. In the embodiment shown in Figure 4, a fixed number of main branch or liner segments 31.Oa are provided in the main branch $15 between the segments 31Cc representing ICDs/hoies/openings 35. In the example of Figure 4, one spacer segment 31Cc is provded betwten the segments 31 Go representing lODs/holes/openings 35. but at least three spacer segments 310a may he preferable.

For example, a vrefl consisting of three hundred holes 35 may require fifty casing senrds or cells 310a, three hundred ICC segments or cells 31Cc, one thousand two hundred liner segments or cells 310a and one thousand two hundred annulus segments or cells 31Gb, making a total of 2,760 segments or cells 310a, 31Gb. SlOc.

This should pose no problem from a computational point of view Whilst a 1:1 relationship between annulus segments or cells 31Db and liner segments or cells 310a may help the numerical solver, it will be appreciated that the user has full flexibility in terms of the number of reservoir grid cells. However, the consequence of having short segments describing the holes is that the coriesponding reservoir cell would also be narrow-. This imbalance between cell sizes may impose sonic imitations when modelling the effect of the acidrock reaction. For a box model study it may he preferable to specify reservoir cells of more or less equal size and then allow several segments to link to the same reservoir cell. If the segmentation workfiow has to he used together with an existing coarseiridded fuii$ield mo-del, seeking a 1:-i ratio by-reducing the number of segments may not be feasible.

in step 2.10 of Figure 3, the pressure drop for each segment or cell 31Cc, 31Gb, 31Cc is calculated, in this exampJe, three components contribute to the pressure drop calculation, namely a friction pressure drop component, a hydrostatic pressure drop component, and an acceleration pressure drop component. These components may be calculated via internal routines in a reservoir simulator, such as Eclipse. However, whilst such reservoir simulators have been found to he chic to adequately determine hydrostatic and acceleration pressure drop components, it has been found that the friction component shouid be beneflciay supphed from an external source due to the impact of drag reducing agents. If Ecpse is used as the reservoir simulator, then the friction pressure drop components may be suppHed via predetermined VFP tables stored in fiat text thee.

in particular, in embodiments of the present invention, friction pressure drop components for a variety of liner geometries and fluid compositions are provided. eg.

comprised in a corresponding pkiraflly of VFP tables 405 (See Figure 5) For example, VFP tables 405 containing appropriate friction pressure drop components are provided for various fluid compositions such as mud, water, water and drag reducing agent (DRA), acid, acid and drag reducing agent, and so on, for each finer geometniAawifi he described in more detsU below, the reservoir simulator can be adapted to switch the current VIP table 405 and thereby the friction pressure drop cornponen being used responsive to changes in fluid composition andlor liner geometry.

niuld ifiction may play an important role in long weDs when injecting fluids such as acid at high rates and there is a need to he able to accurately predict the pressure in the outer part of the waft A d nThole gauge can be used to cafibrate the friction model in the top completion pert and provides confidence that the friction model is equally applicable for the liner segments.

Fluid flow during acid stimulation may exhibit both Newtonian and non Newtonian behaviour, and may involve pipe flow as well as annular flow, in addition to pressure losses through the lCD constrictions. The pressure drop across an Ct is calculated in known reservoir simuiators such as EcDpse by specifying the valve characteristics of the lCD.

in addition, in order to accurately deterrnirre the hydrostatic pressure drop component, the fluid density shouki be allowed to vary with time to simulate injection of fluids with different densities. However, in current reservoir simulators, such as Eclipse, a fluids are treated as a water phase. in this case, the above denaitj change can be modelled by representing mud, acid, drag reducing agent, or the like as a heavy brine while at the same time treating acid as a tracer.

The pressure drops for varying combinations of fluid and pipe geometry can he determined, for example using the equations below. An explanation of the symbols.

used is also found in a giossary at the end.

Lammg[,pIpe flow of mud PVxv PP (1) -0JU1914 x Q (n

-

is the difference n pressure, L is the ength of the pipeiiTher, FV s the pashc viscosity for mud, v, s the ppe vSoo, C) s the diameter, VP s the yield pohit. for mud S and C) s the voiumetric flow rate, Laminar annuiar flow of mud

I

x D) 2O) x (Dc. DJ) a(ii9i4xQ V.. 14 V is the velocity in the annuius, C)0 is the outer diameter for annuar flow ann is the inner diameter for arinuar flow.

LnLQwSm fpyoa x (5) \ LtW0xD / When p is the denelty of the mud 55.

Turbulent annukjs flow of mud x (5) nhoisxfxpxLxcp -4;) Where f as the Fannang fracton factor.

Newtonaan fluid flow an anr:uus = S Fflctaon factor for amnar flow

I (9)

M S

Where Re as the Reynods number. (10)

Re 9. (11) 72;x I) Where s vasco&ty snd E as roughness i / t.2tS . &dij; 3.7x(4 Dj)j iS9i6xxpxQ Ret. (13, Where Re as the Reyn&ds number for annuaar flow, (14) 3. X 8=KC4 (15) Where Re is the Reynokis number for pipe flow. öis the drag reducer shftt factor, K is a DRA model parameter, CA is the DRA co-efficient and a is the DRA model exponent, (16) Where N is a DRA modei parameter.

i9xogRex.)-32A (17) It w be appreciated that the Reynoids number is c&cthated according to the geometry (pipe or annulus). The symbols used are also identified fl a gloaear at the end of this specficaton.

For flow of fluids containing drag reducing agents (DRAs), it should be ensured thai the calculated fricon factor Ves between o bounding curves, defined by the maximum drag reduction asymptote (see equation 17) and the fluid friction without presence of drag reducing agents (see equation 10). denoted in the PKcurvein Figure 6. The parameter W defines the onset of drag reduction and 5 linked to the intersection heteen the drag reduction curve and the lower hounding curve on the Prandti-Karman plot shown in Figure a.

Pressure dron across an lCD 1P=02369xp4)i) (18)

X

Where D:* is the diameter of the openftigs and C is the discharge coefficient of the openings -importantly, the method also comprises tracking ibid fronts in the wefibore system 5 (Step 215 in Figure 3). Tracking of fluid fronts in the we.Ubore system 5 is important for severai reasons. Firstly, different fluids have different densities, which wifl affect the hydrostatic pressure and may thereby limit the. pump rate due to surface pressure constraints, Secondly, as soon as the first acid fr0 reaches the reservoir, the tO flow distribution w11 graduay change as a resutt of the acidfzation process. ihirfly, during shut$ns, fluid fronts may move and induce crossflow between the ner and annulus via the CDs, depending on the pressure profile.

Reservoir simulators can be used to track important parameters such as pressure, phase saturation, and tracer concentration versus time for a given segment.

in embcdirnents of the present invention, tracking of tracer concentrations are used to model the progress of fluid front during the add stimulation process within the weflhcre.

Figure 7 shows an example where each of a plurafity of ces segments 310a in the liner comprise mud 55 at a time T. By time T,, acid 60 has displaced the mud 55 from one segment SICa, ln embodiments of the present invention, the reservoir simulato has been adapted to implement logic that replaces the VEP table 405 (and thereby the friction pressure components) for that segment to reflect its new fluid content, i.e. acid $0 rather than mud 55. In the particular example shown in Figuna 7, the check made is whether the segment contans acid 60 without drag reducing agent.

However, the issue of numerical diffusion is also to be considered, If the requirement for changing a VFP table 405 is that a fluid saturation must reach 100%.

then it has been found that the change invoked in the model will occur later than that wftch is observed during the actual job. Physical mixing in the welibore. is thought to be minimal and displacement therefore occurs in a plug flow manner, which can be evaluated analytically. From experience, and to some. extent influenced by the number of liner cells or segments 310a chosen, a reasonable threshold value for the cutof1 saturation signalling segment fflhng is lower than 100%, e.g. 95%. In other words, when a cell or segment 310a contains 95% of a given fluid, it is assigned a new VFP tablL &5.

Tirnestepping is another parameter that can influence numerical diffusion. In some reservoir simulators, such as Eclipse, the fluid content from one ce/segment is passed on to the next cell/segment even if the previous cell is not entirely filled wtth a particuler fluid. If the reservoir simulator is left to set Its own timeetep, the fluid front will be smeared. This is known as numerical diffusion, instead, in embodiments of the present hivention, the timestep is adjusts to ensure that each cell/segment is filled entirely before fluid Is passed on to the next celL This requires knowledge of the flow rate, the cell volumes end the position of the fluid front. However, these parameters can be determined anytically, thereby allowing the timestep to be altered.

Maior timesteps are needed whenever a particuiarly important event occurs, such as when the pump rate changes, when a new fluid is introduced or when the drag reducing agent concenretion changes. To minimise numerical diFfusion in the top compehon string, the time step must be inked to the pump rate and the cefi volume such that only one segment is ifiled within a given timestep. whenever possible. This time.*steoping is not adequately implemented in current reservoir simulators and may require scripting, for example, in order to tuuy implement this feature, Numerical diffusion in the ner 20 and annulus 50 cannot be controed to the same extent because the fluid front splits up when reaching the first lCD. Furthermore, as soon as acid 00 reaches the first reservoir cefi 31 Oa, the flow distribution changes during each subsequent time step. Here it is necessary to operate with sufficiently small time steps to be able to alter the injectivity regularly by configuring the reservoir simulator with suitable logic. Small time steps, in the order of 30 seconds. are preFerred during the shutin periods deliberately imposed between each rate step to helo evaluate the friction versus rate and to g!VC an indication of the matantaneous skin.

Once the tim&stepping logic has been put in place, the pump schedule can be programmed into the reservoir simulator, as illustrated in Figure 8.

Another step in the method is to account for the ef1ct of the chemical reaction between the acid 60 and the rocks in the geological formation 15, which is step 220 in Figure 3, In embodiments, the starling point is an experimental curve based on linear core floods where the pore volume to breakthrough is correlated as a function of interstitial velocity for a particular acid at a particular concentration and temperature.

Such a curve can then be. fitted by the BuijseGiasbergen expression: I / , \T L, V ° (MI t \. ,4tr, \ (20) Where PV s the pore volume required to breakthrough, Q is the volumetric flow rate.

is time tifi breakthrough. w is the porosity, where V is interstifial v&ocity, end Vlopt S is the interstitial velocity which yields the minimum pare volume to breakthrough, PV,ht,opt.

instead of selecting interstitial velocty as independent variable. it may be preferred to use the Damkbhler number, defined as fbows: c\XD,fXLWk (21)

-

Where Os is the DamkOhler number, D is the effective diffusion coefficient, L.3 is the wormhaie enath and Q. is the volumetric flow rate into a worrnhole.

Figure 9 shows an example of the effect of irection rate on wormhoe growth.

The concept of an optimum Damkdhler number has been described by Fredd eta!. in SPE 38107, presented at the SPE European Formation Damage Conference, The Hague, The Netherlands, 2-3 June (1997), Gdansid, in SPE 54729. presented at the 1999 European Formation Damage Conference. The Hague, The Netherlands, May 3tJune 1 (1999), the content.s of whch are incorporated herein in their entirety.

For strong acids 60 such as hydrochloric acid. the chemical dissolution reaction is fast and the process is therefore mass4ransfer limfted.. The flow rate into each wormhoie depends on the number of active wormholes. Since the Damkohler number depends on the current wcrmhole length. the optimum rate needed to ensure oplimum wonnhole growth is not necessary constant with time.

The number of moles of acid injected into each wormhoie during a time-step j is -fl

-

Where Qwh is the volumetric flow rate into a wormhoie, C is the acid concentration and is the time step.

For the core flood, the wormhoie length at breakThrough is related to the acid pore volume to breakthrough and the number of moles of acid 80 as foows: - »=C tth"' --) t Where Lb is the worrnhole length, is the number of moles of acid, iS the length of the core, PV is the pore volume to breakthrough and 0d is the acid concsntraoon, Eauation 23 is more useftd in differential form to express incremental wormhoie growth from one Ume step to the next: (24) Where is the acid v'olunie.

Equations 19 to 24 above provide a famewc.nk for irnpiementing a wormhole growth model.

A point to consider is the fact that core floods are typicay conducted at constant injection rate, whilst the optimum rate needed to ensure optimum wormhoie growth is not necessarily constant with time. With the use of digital imaging of the acidimtion process, t would in principle be possible to derive an instantaneous wormhole length and relate the growth from one time step to the next to the acid rate flowing into that wormhoie. One proposal is that an altered inection philosophy based on a gradually changing injection rate could be used to reduce the minimum pore volume to breakthrough observed in linear Gore flood experiments.

Another factor is the linear flow direction imposed by standard core fiooding setups, as opposed to the radial flow conditions encountemd in the near.wellhore area.

A publication by McDuff at aL in SPE 134379, presented at the 2010 SPE ATCE, florence italy. 1922 September 2010. the contents of which are incorporated herein in their entirety, illustrated 34) visuaUzation of radial wormhole growth. Conversion of linear core flood data to radial conditions has been addressed by Buijee and Glashergen in SPE. 96892. presented at the 2006 SPE ATCE, Dallas, Te:as, 91 2 October 2005, the contents of which are incorporated herein in their entirety, among others.

The method comprises converting the wormhoie ength into either a skin or a permeabihtv multiper to be mpieuiented in the reservoir smulator. The foowing relation between permeabifltv enhancement, skin, and wcrmhoie length could be used to do this: . (25) Where S reoresents the skin, k is the original permeability, kirn is the permeabi after acid stimulation, is the wormhoie length and c is the wefibore radius.

in a steadystate Peacernanftype inflow model formulation, the skin effect is equivalent teen effective weilbore radius. As long as the skin is positive, this equivalence is usefuL However, for large. negative skins, the calculated equivalent radius may exceed one or more dirnensons of the reservoir ce 310a connected to the segmented wefihore.

instead, it may be oreferable to work with a permeability multiplier. In principle, the acithzalion process alters not only perrneahlllty but also porosity, but permeabHity has by far the largest mpact on the mode ng results. Hence, porosity changes due to dissolution may be ignored. The Peaceman formulation can be modified to account for transient iniiow/outflow effects using a technique described by Archer in SPE 134832, presented at the 2010 SPE ATCE, florence Rely, i$22 September 2010, the contents of which are incorporated herein in their entirety.

in embodiments of the present invention, the parteular choice of wormhole model may be less important. Significantly, embodiments of the present invention include the abity to change the permeability of a ceD based on programmable logic. in this case, the reservoir simulator can be adapted to store the value of the curTent wormhole. length or the corresponding permeaibUity enhancement factor. As such, by performing a comparison against the value of the current wormhoie length, the desired permeabty modification can be triggered.

The abHity to relate the wormhole length to a permeability enhancement ictor in a consistent manner, which will work for a variety of grid sizes, is important for matching observed bottomhole pressures if a comerpoint grid is used, it can be assumed that the same permeability enhancement appLes in cli three directions.

Optionally, the near-wellhore area can be renresented by -a radial grid which gradually turns into a cornorpoint grid.

A simple scaling frctor can then be used, for example. the wormhole length divided by the amest of the three grid size parameters. Advantagenusiy this imposes the constraint that a wc-rrnhole must stay within the reservoir ce connected to the annulus segment. Thus, the permeability modification is performed only for grid ces penetrated by the woW if* these cells are too smali, then the effect of the permeability enhancement wi be too small and the calculated bottonFhoie pressure may remain higher than the observed pressure, In summary, reservoir simulators such as Eclipse are mainly designed for modelling fluid flow in the reservoir, A number of modifications, adaptations and additions to previous reservoir simulators are described above n order to use these reservoir simulators to model acid stimulation, For example; the re*assiqnment of VFP tables based on ccli or segment 310a, 3100, 31Cc fluid content can account for flow of 3 nnNewton.n fludq o drac redug aaw'ts ie mool can then be,muo c optimise the acid stimulation process, e.g. by determining optimal operational parameters, shown as step 225 in Figure 3. As can he seen from Figure 10. the above simulation method can give good approximations, to actual measured pressures both uphole and downhole, In addition, accounting of thermal effects during acid stmfflaton may prove useful in a number of situations, e.g. if acid is injected at a temperature much different from the reservoir temperature or to simulate warm-back. A fiber optic cable with distributed temperature sensing (DTS) could help calibrate a thermal modeL The above embodiments are provided by way of example. It will he appreciated that various modifications may be made to the embodiment described without departing from the scope of the invention.

Glossary A Cross**sectionai area L0id Acid concentration C Discharge coefficient ED Diameter Der Effective, diffusion coefficient Inner diameter for annular flow D0 Quiet dameter for annidar flow Da Damkbher number (transport4nited) Fannng ificflon factor K DRA modS pararr&er L Length of pe L.h Wormhde engLh nd Mdes of add Q Vokimetrk; fkv rate Qh Vdumetrc flow rate nt.o a wormhde

P

PV Pastc vacosty for mud PVbt Pore voume to breakthrough Re Reyndds number RCa Reynokis number for annular flow Re Reynulds number for ppe flow WeHbore radius t Time t Time to breakthrough v Veiocity in annulus v Pipe veboity V Vokne V Acid voiume Pore vtNume of core sampie W DRA modei parameter YP YiSd point for mud Difference o DRA modul exponent o Drag reducer shift parameter c Roughness Por\sitv p Viscosity p Density CLAM&

Claims (10)

1. A method for simulating and/or controUng consecutive flow of a puraty of fluris n a weUbore of arbitrary geometry, the method comprising: S forming, using or providing a model or simulation of the webore, the model or simulation representing the weflbore as a plurality at segments or portions; determining and/or providing one or more friction pressure drop components aasocted with at least one portion or sewnent of the wellbore for the pkiraUty of fluids; calculating pressure drop values for at east one segment or portion and/or between segments. or portions using the one or more friction pressure drop components.

2. The method of cisim 1. wherein the pressure drop values am processed or calculated using a reservoir simulator.

3. The method of claim I or claim 2, wherein the method comprises deterrnrng a pressure response during acid stimulation.

4. The method according to claim 2 or any claim dependent thereon, wherein the method comprises caiculating the one or more friction pressure drop component independently of and/or separately from the reservoir simulator and inputting the friction pressure drop component(s) into the reservoir simulator.

5. The method according to any preceding claim, wherein the friction pressure drop components are comprised in and/or are provided in the form of one or more vertical flow profe (VFP) tables.

6. The method according to any preceding claim, wherein the method comprises determining or providing a plurality of friction pressure drop components or VFP tables for at least one portion or segment, wherein each of the friction pressure drop components or VFT tables are associated with at least one of: a different fluid a different fluid composition, a different fluid concentration. and'or a different liner geometry.

7. The method of ciaim 6. wherein the method comprises dynamically switching, updating or selecUng VEP tables end/or fliction pressure drop components during operation or use of the model or simulation responsive to or dependent on changes in fluid, fluid composition, ner geometry and/or fluid concentration.

8. The method according to any prcceding claim, wherein the method comprises modemg or varying the fluid density and/or fluid concentration and/or composition for one or more segments or portions of the modeL

9. The method of claim 8 wherein the fluid density is modelled or varied by varying a property or parameter of the fluid in the simulation or model, such as a sait concentration.

10. The method of any preceding claim., wherein the method comprises determining, modelling and/or tracking one or more fluid fronts in the model or sirr.uletlon.11 The method according to claim 10, wherein the method comprises modeing.determining and/or trackino fluid fronts by representing the fluid front(s) using a tracer or tracer concentration.12. The method according to any preceding claim. wherein the weilbore comprises a met, the liner comprising a plurality of holes or apertures and the total hole $5 area per length unit of the liner is greate at a toe or second portion of the injection webore than at a heel or first porbon of the injection section of the wel bore..13. A processing device or simulator for simulating and/or modelling a webore, the processing device or simulator being configured to mode' or simulate the weUbore using the method of any of claims 1 to 1$.14. A controller for controUing apparatus for performing a weilbore intervention or process, the controfler comprising or being configured to communicate with the processing device according to claim 13.15. A computer program product for at least partially, and optionally wholly.implementing the method of any of claims I to 12 andIor the apparatus of claim l3orclalm 14.18. A carrier medium or processing apparatus comprising or programmed with the computer program product of claim 15.17. A method for simulating and/or controlling consecutive flow of a plurallty of fluids In a ltoie of arbitrary geometsy substantially as descilbed herein In relation to the drawings.